In this thesis, we study the growth of Sobolev norms of global solutions of solutions to nonlinear Schrödinger type equations which we can't bound from above by energy conservation. The growth of such norms gives a ...

We provide two algorithms to solve branching from K to M for the real split reductive group of type A, one inductive and one related to semistandard Young tableaux. The results extend to branching from Ke to M Ke for the ...

The classical Brill-Noether theorems count the dimension of the family of maps from a general curve of genus g to non-degenerate curves of degree d in projective space Pr. These theorems can be extended to include ramification ...

Broken Lefschetz fibrations are a new way to depict smooth 4-manifolds and to investigate their topology; for instance, Perutz defines invariants of 4-manifolds by counting J-holomorphic sections of these fibrations. The ...

This thesis will be concerned with the geometry of minimal submanifolds in certain Riemannian manifolds which possess some special geometric structure. Those Riemannian manifolds will fall into one of the following categories: ...

The Greene-Kleitman theorem says that the lengths of chains and antichains in any poset are intimately related via an integer partition, but very little is known about the partition [lambda](P) for most posets P. Our first ...

Inspired by the work of Lusztig, we apply the theory of character sheaves on a symmetric space (h la Ginzburg and Grojnowski) to the problem of determining the spherical functions (averages of the irreducible characters) ...

This thesis concerns combinatorial and enumerative aspects of different classes of posets and polytopes. The first part concerns the finite Eulerian posets which are binomial, Sheffer or triangular. These important classes ...

Let g be a complex, reductive Lie algebra. We prove a theorem parametrizing the set of nilpotent orbits in g in terms of even nilpotent orbits of subalgebras of g and show how to determine these subalgebras and how to ...